Journal ArticleDOI
New fast algorithm to compute two-dimensional discrete Hartley transform
TLDR
A new fast algorithm for computing the two-dimensional discrete Hartley transform that requires the lowest number of multiplications compared with other related algorithms is presented.Abstract:
A new fast algorithm for computing the two-dimensional discrete Hartley transform is presented. This algorithm requires the lowest number of multiplications compared with other related algorithms.read more
Citations
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Journal ArticleDOI
Fourier volume rendering
TL;DR: A volume rendering technique that operates on a frequency domain representation of the data set and that efficiently generates line integral projections of the spatial data it represents that can be rendered at a significantly lower computational cost than images generated by current volume rendering techniques is presented.
Journal ArticleDOI
Radix-3 $\,\times\,$ 3 Algorithm for The 2-D Discrete Hartley Transform
TL;DR: A vector-radix algorithm for the fast computation of a 2-D discrete Hartley transform (DHT) and a radix-3 times 3 decimation in frequency algorithm for data sequences whose length is a power of three is developed.
Proceedings ArticleDOI
Three algorithms for computing the 2-D discrete Hartley transform
Artyom M. Grigoryan,S.S. Agaian +1 more
TL;DR: Three algorithms based on the method of vector and paired transforms for dividing the computation of the nonseparable two-dimensional discrete Hartley transform into the "minimal" number of the one-dimensional (1-D) DHT's are presented.
Book ChapterDOI
A Fourier Technique for Volume Rendering
Thomas Malzbender,Fred Kitson +1 more
TL;DR: A technique for using the Fourier Projection Slice Theorem for display of volume data which can achieve a complexity of 1–3 orders of magnitude less than either a screen space or object space volume rendering techniques.
Journal ArticleDOI
Split-radix algorithm for 2-D discrete Hartley transform
TL;DR: This paper presents a fast split-radix algorithm for the two-dimensional discrete Hartley transform that achieves substantial savings on the number of operations and provides a wider range of choices on different transform sizes.
References
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Journal ArticleDOI
Fast algorithms for the discrete W transform and for the discrete Fourier transform
TL;DR: A systematic method of sparse matrix factorization is developed for all four versions of the discrete W transform, the discrete cosine transform, and the discrete sine transform as well as for the discrete Fourier transform, which makes new algorithms more efficient than conventional algorithms.
Book
The Hartley transform
TL;DR: The author describes the fast algorithm he discovered for spectral analysis and indeed any purpose to which Fourier Transforms and the Fast Fourier Transform are normally applied.
Journal ArticleDOI
Fast two-dimensional Hartley transform
TL;DR: The fast Hartley transform algorithm as discussed by the authors offers an alternative to the fast Fourier transform, with the advantages of not requiring complex arithmetic or a sign change of i to distinguish inverse transformation from direct.
Journal ArticleDOI
A new efficient algorithm to compute the two-dimensional discrete Fourier transform
TL;DR: It is shown that the number of distinct N-point DFTs needed to calculate N*N-point two-dimensional DFT’s is equal to thenumber of linear congruences spanning the N-N grid.
Journal ArticleDOI
Vector Hartley transform
TL;DR: The fast Hartley transform provides the same information as the fast Fourier transform (FFT) but with greater speed and efficiency when the input data are real.